Least Common Multiple (LCM) of 106 and 194
The least common multiple (LCM) of 106 and 194 is 10282.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 106 and 194?
First, calculate the GCD of 106 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 194 = 0 remainder 106 |
| 2 | 194 ÷ 106 = 1 remainder 88 |
| 3 | 106 ÷ 88 = 1 remainder 18 |
| 4 | 88 ÷ 18 = 4 remainder 16 |
| 5 | 18 ÷ 16 = 1 remainder 2 |
| 6 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 49 | 1225 |
| 154 and 150 | 11550 |
| 14 and 197 | 2758 |
| 129 and 136 | 17544 |
| 111 and 35 | 3885 |